order of individual FFTs for calculating `numpy.fft.irfftn`

[vtavana]

For numpy.fft.fftn and numpy.fft.ifftn, individual FFTs over axes are performed in reverse order.

Similarly, for numpy.fft.rfftn, individual FFTs are performed in reverse order.

However, for numpy.fft.irfftn individual FFTs are performed in forward order.

Currently we compute complex-to-complex FFT for axes[0], axes[1], .. axes[-2] and then one final complex-to-real FFT for axes[-1].
Should it be changed to complex-to-complex FFT for axes[-2], axes[-3], .. axes[0] and one final complex-to-real FFT for axes[-1] (still keeping the complex-to-real FFT over last axis)?

In general, order is not important when calculating complex-to-complex FFTs. However, when we pass s and axes parameters (with repeated indices in axes), order can affect the final shape of the array.

[mhvk]

Hmm, good question. Maybe it is more logical to also use forward order for ifft?

[vtavana]

@mhvk yes, what you said make more sense.

In general, order is only important when there is repeated indices in axes, I noticed that SciPy does not allow repeated axes at all. I do not if there are real use cases for repeated axes, if not maybe NumPy can also raises an error when repeated axes are passed.